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Optimization in Arrangements

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STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

Many problems can be formulated as the optimization of functions in R 2 which are implicitly defined by an arrangement of lines, halfplanes, or points, for example linear programming in the plane. We present an efficient general approach to find the optimum exactly, for a wide range of functions that possess certain useful properties. To illustrate the value of this approach, we give a variety of applications in which we speed up or simplify the best known algorithms. These include algorithms for finding robust geometric medians (such as the Tukey Median), robust regression lines, and ham-sandwich cuts.

Chargé de recherches du FNRS à l’Université Libre de Bruxelles

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, USA

    Stefan Langerman

  2. Computer Science, Rutgers University, USA

    William Steiger

Authors
  1. Stefan Langerman
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  2. William Steiger
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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© 2003 Springer-Verlag Berlin Heidelberg

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Langerman, S., Steiger, W. (2003). Optimization in Arrangements. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_6

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  • DOI: https://doi.org/10.1007/3-540-36494-3_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

  • eBook Packages: Springer Book Archive

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